Addendum to the Second Printing BCPI logo billcutlerpuzzles.com

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October 10, 1988

This second printing of "HOLEY 6-PIECE BURR !" was prepared for duplication by Rex Shudde using PC TEX and PICTEX. The text, drawings, and computer output have been redone but have essentially the same content as the first printing.

The following are recent developments in the analysis of 6-piece burrs:

"Level" usage

The second version of the program BURR6 uses a definition of level which does not allow pieces to move different amounts in the same direction in one move or "level". (See comment 2. on page 6). The program allows for use of the older definition as an option.

Challenge Questions

The "Challenge Questions" section consists of questions which I do not know the answer to (though I may have strong thoughts on the subject). In particular, I do not know of a 6-piece burr with normal, cubic-cut pieces which requires a twist move. I would be quite surprised if there were one, but have not attempted to prove this. Peter Marineau and Bruce Love sent designs which are solvable using length 10 pieces, but are not solvable using length 12 pieces. Peter Marineau sent a proof that this is the longest length for which there is a difference, but I am not completely convinced of this answer. For notchable burrs, no solution exists with length 10 pieces which is not a solution for length 12 or longer pieces. Peter Marineau's record of a unique level-9 solution still holds at this date. Bruce Love has a design, "Love's Dozen", which is level-12, but not unique. This is now the record for non-unique solutions.

Notchable Analysis

A complete analysis of 13,354,991 essentially different notchable assemblies was completed by computer runs from March to June of 1987. The highest levels found were: Level-10 (non-unique) - 2 solutions, one with 9 holes, and the other with 11 holes. Level-5 (unique) - many such solutions. The results will be published in a sequel to this booklet entitled: "Holey 6-Piece Burr - The Notchable Case".

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